If $ f_{1}(x,y)$ and $ f_{2}(x,y)$ are two homogeneous polynomials then prove that : $ \frac{f_{1}(x,y)+f_{2}(x,y)}{xf_{1}(x,y)+yf_{2}(x,y)}$ is homogeneous.

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# Is $x f(x,y)+y g(x,y)$ homogeneous if f and g homogeneous?

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If $ f_{1}(x,y)$ and $ f_{2}(x,y)$ are two homogeneous polynomials then prove that : $ \frac{f_{1}(x,y)+f_{2}(x,y)}{xf_{1}(x,y)+yf_{2}(x,y)}$ is homogeneous.

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